Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.7

Lesson 7.87.8 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can plot ordered pairs in all four quadrants of the coordinate plane, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 7.8. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
QuadrantSpanish: Cuadrante One of the four parts of a coordinate grid, numbered I to IV. I (+, +) top-right, II (-, +) top-left, III (-, -) bottom-left, IV (+, -) bottom-right
Negative coordinateSpanish: Coordenada negativa A coordinate less than zero. It means left or below the center point. (-3, 2) means 3 left and 2 up from the origin
ReflectionSpanish: Reflexión A flipped, mirror image across a line. (3, 2) reflected over the y-axis is (-3, 2) — same distance, opposite side
AxisSpanish: Eje One of the two number lines that frame a graph: the x-axis runs across, the y-axis runs up and down. The x-axis goes left-right; the y-axis goes up-down; they cross at (0, 0)
IntegerSpanish: Número entero Whole numbers and their opposites, like -2, -1, 0, 1, 2. ..., -3, -2, -1, 0, 1, 2, 3, ...

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Point A is 4 units left of the y-axis and 2.5 units down from the x-axis. Name point A and its quadrant.

  1. Turn left 4 into an x-coordinate: left 4 → x = −4
  2. Turn down 2.5 into a y-coordinate: down 2.5 → y = −2.5
  3. Write the ordered pair, x first: (−4, −2.5)
  4. Use the signs to name the quadrant: (−, −) → Quadrant III
  5. Point A is (−4, −2.5). It is in Quadrant III.
  6. Which quadrant is the point (0, −5) in?
  7. Read x. Do not move left or right: x = 0
  8. Read y. Move down 5 units: y = −5 → down 5
  9. Decide if the point is in a quadrant: on the y-axis → no quadrant
  10. (0, −5) is on the y-axis. It is not in any quadrant.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Plot the point (−5, 2). Name the quadrant it is in.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • In Quadrant , the x-coordinate is and the y-coordinate is . I know (-3, -4) is in Quadrant because both coordinates are .

Word bank QuadrantNegative coordinateReflectionAxisIntegerquadrantpositivenegativex-coordinatey-coordinateleftright

Watch out!A common mistake

A common mistake in Ordered Pairs in All Four Quadrants is matching each sign to the wrong axis

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.7

Lesson 7.87.8 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can plot ordered pairs in all four quadrants of the coordinate plane, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 7.8. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    0−5−4−3−2−112345−5−4−3−2−112345B
    Point B, right and down from the origin.

    Point B is 3.5 units right of the y-axis and 4 units down from the x-axis. Name point B and its quadrant.

    1. 1Turn right 3.5 into an x-coordinate.
    2. 2What is the y-coordinate of B?
    3. 3Which quadrant is B in?
    Final answer:
  2. 2Complete each step, then write the final answer.
    0−5−4−3−2−112345−4−3−2−11234(−4, 0)
    The point sits on an axis.

    Plot the point (−4, 0). Which quadrant is it in?

    1. 1Which way do we move for x = −4? For y = 0?
    2. 2Every point on the x-axis has the same y-coordinate. What is it?
    3. 3Why is (−4, 0) not in Quadrant II or Quadrant III?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Which quadrant is the point (−0.5, 8) in?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Point R is in Quadrant IV. It is 7 units from the y-axis and 2 units from the x-axis. What is the y-coordinate of R?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A diver starts at a dock at (0, 0). She swims 4 units west, then 3 units east, then 6 units south. East and north are positive. Which quadrant is she in now?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Max says: "If x and y have different signs, the point is in Quadrant II." Test his rule on (3, −7). Which quadrant is (3, −7) really in?

    Show your work
    Final answer:

Explain your thinkingMax only checked if the signs were different. What else must you check? Compare (3, −7) and (−3, 7).

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help